Smooth solutions of non-linear stochastic partial differential equations driven by multiplicative noises  

作　　者：ZHANG XiCheng School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China 

出　　处：《Science China Mathematics》2010年第11期2949-2972,共24页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 10971076, 10871215)

摘　　要：In this paper, we study the regularity of solutions of nonlinear stochastic partial differential equations (SPDEs) with multiplicative noises in the framework of Hilbert scales. Then we apply our abstract result to several typical nonlinear SPDEs such as stochastic Burgers and Ginzburg-Landau equations on the real line, stochastic 2D Navier-Stokes equations (SNSEs) in the whole space and a stochastic tamed 3D Navier-Stokes equation in the whole space, and obtain the existence of their smooth solutions respectively. In particular, we also get the existence of local smooth solutions for 3D SNSEs.In this paper, we study the regularity of solutions of nonlinear stochastic partial differential equations (SPDEs) with multiplicative noises in the framework of Hilbert scales. Then we apply our abstract result to several typical nonlinear SPDEs such as stochastic Burgers and Ginzburg-Landau equations on the real line, stochastic 2D Navier-Stokes equations (SNSEs) in the whole space and a stochastic tamed 3D Navier-Stokes equation in the whole space, and obtain the existence of their smooth solutions respectively. In particular, we also get the existence of local smooth solutions for 3D SNSEs.

关 键 词：SMOOTH solutions STOCHASTIC PARTIAL differential EQUATIONS STOCHASTIC NAVIER-STOKES EQUATIONS 

分 类 号：O211.63[理学—概率论与数理统计]